## Introduction: Inverted Sundial on My Balcony

I’m fascinated by sundials. I like their simplicity and the way they connect us with the universe. When I moved to this place with a south-facing balcony, I couldn’t resist to build a sundial on it.

More precisely, I’ve built an inverted sundial. The point where we read the current time is fixed and shadow lines corresponding to each hour move around it.

## Step 1: What’s an Inverted Sundial?

To each hour corresponds a line of shadow that moves over time. You read the time by comparing the position of the shadow lines with a fixed point that indicates the current time (see the photo in the previous part).

You can build such a sundial by starting from a common vertical declining sundial, as shown in the first schema, and then applying the following changes:

- extend the style upward,
- find its intersection point with the ground (in green on the second schema),
- extend the lines upward.

In my case, the vertical surface (dotted green line on the second schema) is my balcony railing and the horizontal surface is the balcony ground. We read the time by comparing the position of the shadow lines with the green point.

Credits for the schemes: Cadrans solaires originaux- www.cadrans-solaires.fr

## Step 2: Compute the Sundial

First, I had to compute the position of the hour lines according to the orientation of my balcony railing. To do that, I’ve used the website SunEarthTools.com, which can give you the position of the sun for any given location and time.

All the angles given by this tool are relative to the north, so I had to find the angle between my balcony railing and the north. I found it by reporting the time when the sun was exactly facing the balcony (for me this was easy to find: it was when the shadow of a vertical object was perfectly aligned with the square tiles of my balcony) on SunEarthTools.com. Then the tool gave me orientation of the sun (aka its “azimuth”) at that time.

Once I knew the balcony orientation I was able to compute the orientation of the sun for every hour of the day, relative to my balcony orientation.

Actually, because of the apparent motion of the sun throughout the year, I don’t get only one intersection point between a ray light and the balcony railing, for a given hour. I get a different point per day. That’s why we have hour “lines” and not hour “points”. So, to define these lines I had to pick two points per hour: one at the winter solstice and one at the summer solstice. The resulting hour line is an approximation of the hour “points” because the earth orbit is not a perfect circle. Consequently the precision of the line is ±15min.

To sum up, for each hour of winter solstice I asked SunEarthTools.com the position of the sun (its azimuth and elevation), and corrected the azimuth to make it relative to the orientation of the balcony. Then I did the same for the summer solstice.

Then, I had to find the intersection of these rays of light with my balcony railing (schemes 2 and 3). Knowing the distance OA of the reading point A with the railing, and the azimuth of the sun, I can find the distance OX of the X coordinate of the ray light intersection with the balcony railing. Similarly, knowing the distance OA and the elevation of the sun, I can find the distance OY of the Y coordinate of the ray light intersection with the balcony railing.

## Step 3: Build the Sundial

Because I rent my apartment I wanted to find a way to build the sundial such that it is easy to “unbuild” when I leave. Therefore I decided to use some thin adhesive tape (3 mm) to mark the hour lines on the railing.

I only needed a meter, a pen, the adhesive tape and scissors to make the sundial.

I reported the points computed at the previous step on the balcony railing and then linked them with the adhesive tape.

Finally, I also added roman numbers below each hour line. In case you live in a timezone that uses “daylight saving time”, you should put the numbers corresponding to the winter time at the bottom of the lines, and the numbers corresponding to the summer time at the top.

## Step 4: Read Time

When the sun shines, look at the shadow of the lines on the ground. In my case the “current time” point is the tile intersection on the photos. On the first picture we can see that the line for 11:00 just passed over the “current time” point. It must be something like 11:05.

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## Comments

This is awesome! I love sundials but I've always been slightly apprehensive of the math. But you make it look so easy!